Project ForgeStrength of Materials
Stress & Strain
GATE 2017
Expert
A rectangular region in a solid is in a state of plane strain. The (x,y) coordinates of the corners of the undeformed rectangle are given by P(0,0), Q(4,0), R(4,3), S(0,3). The rectangle is subjected to uniform strains, εₓₓ=0.001, ε_yy=0.002, γₓy=0.003. The deformed length of the elongated diagonal, upto three decimal places, is __________ units.
5.014 units(± 0.002 accepted)
Explanation
Diagonal PR: length 5, direction cosines l=4/5=0.8, m=3/5=0.6. Normal strain along PR: εₙ = εₓₓl²+ε_yym²+γₓylm = 0.001(0.64)+0.002(0.36)+0.003(0.8)(0.6) = 0.00064+0.00072+0.00144 = 0.0028. Deformed length = 5×(1+0.0028) ≈ 5.014.
Source: GATE ME 2017 Session 1 (ME-1) (2017)
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